Details

Time bar (total: 1.7m)

sample232.0ms

Algorithm
intervals
Results
83.0ms58×body1280valid
76.0ms41×body640valid
38.0ms176×body80valid
17.0ms26×body320valid
2.0ms5×body160valid

simplify128.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
128.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ x (tan B))
0.1b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (/ x (tan B)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
279×times-frac
232×add-sqr-sqrt
224×*-un-lft-identity
215×add-cube-cbrt
182×prod-diff
31×div-inv
14×tan-quot associate-/r/
13×fma-neg
9×add-exp-log
7×add-cbrt-cube
6×associate-/r* associate-/l* difference-of-squares
5×add-log-exp
4×pow1
3×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u distribute-lft-out--
2×cbrt-undiv clear-num frac-2neg
1×rec-exp sub-neg flip3-- diff-log 1-exp frac-sub pow-flip flip-- inv-pow
Counts
3 → 285
Calls
3 calls:
Slowest
36.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
6.0ms
(/ x (tan B))
5.0ms
(/ 1 (sin B))

series311.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
145.0ms
(/ x (tan B))
143.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
24.0ms
(/ 1 (sin B))

simplify1.2m

Counts
456 → 294
Calls
456 calls:
Slowest
801.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ (cbrt x) (cbrt (tan B))) (/ (* (cbrt x) (cbrt x)) (* (cbrt (tan B)) (cbrt (tan B)))))))
616.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
583.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
578.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
575.0ms
(fma (/ 1 (sqrt (sin B))) (/ 1 (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune3.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos B) (sin B)) x)
0.2b
(/ (cos B) (sin B))
0.1b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (* (/ (cos B) (sin B)) x))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
46×times-frac
42×*-un-lft-identity add-cube-cbrt
15×add-exp-log
13×add-cbrt-cube fma-neg associate-*l* prod-diff
7×pow1
6×associate-/r* associate-/l* add-log-exp
5×div-inv
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-*r* associate-*l/
2×clear-num frac-2neg prod-exp cbrt-unprod unswap-sqr
1×rec-exp sub-neg flip3-- diff-log 1-exp pow-prod-down *-commutative frac-sub pow-flip flip-- inv-pow sub-div
Counts
4 → 142
Calls
4 calls:
Slowest
36.0ms
(- (/ 1 (sin B)) (* (/ (cos B) (sin B)) x))
14.0ms
(* (/ (cos B) (sin B)) x)
9.0ms
(/ (cos B) (sin B))
6.0ms
(/ 1 (sin B))

series341.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
169.0ms
(- (/ 1 (sin B)) (* (/ (cos B) (sin B)) x))
123.0ms
(* (/ (cos B) (sin B)) x)
26.0ms
(/ (cos B) (sin B))
23.0ms
(/ 1 (sin B))

simplify6.2s

Counts
130 → 154
Calls
130 calls:
Slowest
475.0ms
(/ (* (* (cos B) (cos B)) (cos B)) (* (* (sin B) (sin B)) (sin B)))
407.0ms
(- (/ 1 B) (+ (* 1/3 B) (* 1/45 (pow B 3))))
338.0ms
(* (* (* (/ (cos B) (sin B)) (/ (cos B) (sin B))) (/ (cos B) (sin B))) (* (* x x) x))
246.0ms
(/ (exp (/ 1 (sin B))) (exp (* (/ (cos B) (sin B)) x)))
207.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ x (sin B)) (cos B))
0.1b
(/ 1 (sin B))
0.1b
(/ x (sin B))
0.0b
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
46×times-frac
42×*-un-lft-identity add-cube-cbrt
15×add-exp-log
13×add-cbrt-cube fma-neg associate-*l* prod-diff
7×pow1
6×associate-/r* associate-/l* add-log-exp
5×div-inv
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-*r* associate-*l/
2×clear-num frac-2neg prod-exp cbrt-unprod unswap-sqr
1×rec-exp sub-neg flip3-- diff-log 1-exp pow-prod-down *-commutative frac-sub pow-flip flip-- inv-pow sub-div
Counts
4 → 142
Calls
4 calls:
Slowest
26.0ms
(* (/ x (sin B)) (cos B))
25.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
8.0ms
(/ 1 (sin B))
5.0ms
(/ x (sin B))

series317.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(* (/ x (sin B)) (cos B))
118.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
54.0ms
(/ x (sin B))
18.0ms
(/ 1 (sin B))

simplify5.5s

Counts
130 → 154
Calls
130 calls:
Slowest
386.0ms
(/ (* (* x x) x) (* (* (sin B) (sin B)) (sin B)))
225.0ms
(* (* (* (/ x (sin B)) (/ x (sin B))) (/ x (sin B))) (* (* (cos B) (cos B)) (cos B)))
209.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
207.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
196.0ms
(/ (exp (/ 1 (sin B))) (exp (* (/ x (sin B)) (cos B))))

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (tan B))
0.6b
(cbrt (tan B))
0.6b
(cbrt (tan B))
0.5b
(* (cbrt (tan B)) (cbrt (tan B)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
7×cbrt-div tan-quot
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 91
Calls
4 calls:
Slowest
25.0ms
(* (cbrt (tan B)) (cbrt (tan B)))
2.0ms
(cbrt (tan B))
2.0ms
(cbrt (tan B))
2.0ms
(cbrt (tan B))

series682.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
199.0ms
(* (cbrt (tan B)) (cbrt (tan B)))
175.0ms
(cbrt (tan B))
155.0ms
(cbrt (tan B))
153.0ms
(cbrt (tan B))

simplify2.1s

Counts
72 → 103
Calls
72 calls:
Slowest
284.0ms
(pow (/ (pow (sin B) 2) (pow (cos B) 2)) 1/3)
251.0ms
(pow (/ (pow (sin B) 2) (pow (cos B) 2)) 1/3)
227.0ms
(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))
225.0ms
(+ (pow B 2/3) (+ (* 31/405 (pow (pow B 14) 1/3)) (* 2/9 (pow (pow B 8) 1/3))))
225.0ms
(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes147.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch1.0ms

end0.0ms

sample8.5s

Algorithm
intervals
Results
3.0s1741×body1280valid
2.6s1450×body640valid
1.8s4939×body80valid
650.0ms687×body320valid
182.0ms365×body160valid